Subquadratic space complexity Gaussian normal basis multipliers over GF(2m) based on Dickson–Karatsuba decomposition


Gaussian normal basis (GNB) of the even-type is popularly employed in elliptic curve cryptosystems. Efficient GNB multipliers might be realised by Toeplitz matrix-vector decomposition to understand subquadratic area complexity architectures. In this study, Dickson polynomial representation is proposed as another approach to represent an GNB of characteristic 2. The authors have derived a unique recursive Dickson-Karatsuba decomposition to attain a subquadratic space-complexity parallel GNB multiplier. By theoretical analysis, it's shown that the proposed subquadratic multiplier saves regarding fiftypercent bit-multiplications compared with the corresponding subquadratic GNB multiplication using Toeplitz matrix-vector product approach.

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